Download WEAK NOUN PHRASES: SEMANTICS AND SYNTAX

WEAK NOUN PHRASES: SEMANTICS AND SYNTAX
Barbara H. Partee
UMASS, Amherst
mailto:[email protected]
В работе рассматриваются современные
семантические анализы слабых ИГ (a unicorn, more
than one unicorn, no unicorn). Главным свойством
этого типа ИГ является возможность обозначать
свойства, т.е. интенсиализированные множества
индивидов.
1. NPs as Generalized Quantifiers.
Classic formal semantics adopted Montague’s
proposal (Montague 1973) for the semantics of Noun
Phrases (NPs). Every NP was interpreted as denoting a
set of sets (strictly, a set of properties; we return to the
distinction later.) In Montague’s type theory, the
semantic type corresponding to NPs is (e → t) → t:
characteristic functions for sets of sets of entities.
Some NP interpretations:
John
λP[P(j)]
(the set of all of John’s properties)
John walks
λP[P(j)] (walk) ≡ walk (j)
(function-argument application)
every student
λP∀x[student(x) → P(x)]
(the set of all of properties that every student has)
every student walks
λP∀x[student(x) → P(x)] (walk) ≡
≡ ∀x[student(x) → walk(x)]
(function-argument application)
a student
λP∃x[student(x) & P(x)]
(the set of all of properties
that at least one student has)
the king
λP [∃x[king(x) & ∀y ( king(y) → y = x) & P(x))]
(the set of properties
which the one and only king has)
The meaning of a Determiner like the, a, every is
then a relation between sets, or a function which applies
to one set (the interpretation of the common noun CN)
to give a function from sets to truth values, or
equivalently, a set of sets (the interpretation of the NP).
Typical case:
S
/ \
NP VP
/
\ walks
DET CN
every student
CN: type e → t
VP: type e → t
DET: interpreted as a function which applies to
CN meaning to give a generalized quantifier, a function
which applies to VP meaning to give truth value), type:
(e → t) → ((e → t) → t)
NP: type (e → t) → t
Sometimes it is simpler to think about DET
meanings in relational terms:
Every:
as a relation between sets A and B
(“Every A B”): A ⊆ B
So ‘Every man walks’ means: || man || ⊆ || walk ||
Some, a: A ∩ B ≠ ∅ .
No: A ∩ B = ∅ .
Most (not first-order expressible):
| A ∩ B | > |A - B|.
From the relational view, it is a small step to
determiners as functions. For example, applying the
function interpreting every to argument set A gives as
result {B| A ⊆ B}: the set of all sets that contain A as a
subset. Equivalently: ║Every║(A) = {B| ∀x ( x ∈ A
→ x ∈ B)}. Equivalently: ║Every║ = λQ[λP[∀x ( Q(x)
→ P(x) )]].
Some, a: takes as argument a set A and gives as
result {B| A ∩ B ≠ ∅ }.
║a║ = λQ[λP[∃x ( Q(x) & P(x) )]]
Given this background, we consider
interpretation of NPs as “weak” or “strong”.
the
2. “Weak” determiners and existential sentences.
Data: OK, normal:
There is a new problem. (1)
There are three semantics textbooks. (2)
Neither correct answer is an even number
Neither even number is a correct answer.
≠
Many factors make it difficult to apply to Russian
the test we used for English. A better, but provably
equivalent, semantic test comes from symmetry:
There are many unstable governments. (3)
Anomalous, not OK, or not OK without
special interpretations:
#There is every linguistics student. (4)
(a) Na kuxne
tri černye koški ≡
In kitchen
black
3
≡ Tri koški na kuxne
3
#There are most democratic governments. (5)
Semantic explanation, with roots in (Milsark
1977), formal development by (Barwise and Cooper
1981) and by Keenan.
Definition (Keenan 1987): A determiner D is a
basic existential determiner if for all models M and all
A,B ⊆ E, D(A)(B) = D(A∩B)(E). Natural language
test: “Det CN VP” is true iff “Det CN which VP
exist(s)” is true. A determiner D is existential if it is a
basic existential determiner or it is built up from basic
existential determiners by Boolean combinations (and,
or, not).
Examples:
(i) Three is a basic existential determiner because
it is true that: Three cats are in the tree iff three cats
which are in the tree exist.
(ii) Every is not a basic existential determiner. If
there are 5 cats, of which 3 are in the tree, “Every cat is
in the tree” is false but “Every cat which is in the tree
exists” is true.
Basic existential determiners = symmetric
determiners.
We can prove, given that all determiners are
conservative (Barwise and Cooper 1981), that Keenan’s
basic existential determiners are exactly the symmetric
determiners.
Symmetry: A determiner D is symmetric iff for
all A, B, D(A)(B) ≡ D(B)(A).
Testing:
Weak (symmetric): Three cats are in the kitchen
≡ Three things in the kitchen are cats.
More than 5 students are women ≡ More than 5
women are students.
Strong (non-symmetric): Every Zhiguli is a
Russian car ≠ Every Russian car is a Zhiguli.
černye.
cats in kitchen
#There are both computers. (6)
#There is the solution. (# With “existential” there
; OK with locative there.) (7)
cats
(b) Na kuxne
black
vse černye koški ≠
In kitchen all black cats
≠ Vse koški na kuxne černye.
all cats in kitchen
black (8)
It is also harder to find constructions in Russian
which allow only weak determiners, for a variety of
reasons. There do seem to be at least two:
(i) The context in (9) is modeled on the English
weak-NP context involving have with relational nouns,
which I've discussed in print (Partee 1999). It’s
important that the noun is relational.
U nego
est' ____
at him.GEN is
sestra
____
/ sestry
/ sester
sister.NOM.SG / sister.GEN.SG / sister.GEN.PL
‘He has ____ sister(s).’ (9)
The context in (9) clearly accepts weak Dets
including cardinal numbers, nikakoj sestry ‘no sister’, ni
odnoj sestry ‘not a single sister’, nikakix sester ‘no
sisters’ (the negative ones require replacement of est'
‘be’ by net ‘not-be’, of course), neskol'ko ‘several’,
mnogo ‘many’, nemnogo ‘few’. And it clearly rejects
strong Dets vse ‘all’, mnogie ‘most’, eti ‘those’.
(ii) Another context which allows only weak
determiners, in at least English, Polish, and Russian is
the following (Joanna Blaszczak, p.c.):
dom
s
______ oknom/oknami
a house with _____
window/windows (10)
Caution: as noted by Milsark (1974, 1977), many
English determiners seem to have both weak and strong
readings, and the same is undoubtedly true of Russian.
3. Property-type NP interpretations
While some differences in the possible occurrence
of ‘weak’ and ‘strong’ NPs can be accounted for by
drawing semantic distinctions within the theory of
generalized quantifiers, as in the account above, it has
been argued that in some cases, weak NPs are really of
“property type” (an intensional variant of type e → t),
rather than generalized quantifiers. Property-type
analyses of various “weak NPs” are becoming
increasingly common in Western formal semantics, and
may have application to some problems in Russian
semantics, including the Russian Genitive of Negation
(section 4.)
Montague (1973) argued that the same semantic
effect can be achieved with a simpler syntax, if NPs as a
unicorn express Generalized Quantifiers. In argument
position, every category gets an intensional operator “^”
applied to it (i.e. functions apply to the intensions of
their arguments).
For Montague, the relation between seek and try
to find is captured not by decomposition but by a
meaning postulate.
Meaning postulate:
3.1. Zimmermann 1993 on intensional verbs.
Zimmermann (1993) argues that Montague’s
analysis of verbs like seek (“intensional transitive
verbs”, or “opaque verbs”) as taking arguments of type
“intension
of
Generalized
Quantifier”,
or
<s,<s,<e,t>>,t> is incorrect. He argues that the NP
objects of opaque verbs should be semantically
interpreted as properties (or type <s,<e,t>>.)
3.1.1. The fundamental properties of intensional
contexts.
Caroline found a unicorn.
(extensional, unambiguous)
(11)
Caroline sought a unicorn.
(intensional, ambiguous)
(12)
Sentences with seek are ambiguous between a
specific and a non-specific reading (or transparent vs.
opaque reading). (1) is unambiguous, (2) is ambiguous.
On the opaque reading of (2), the existence of a
unicorn is not entailed.
Substitution
of
extensionally
equivalent
expressions in an intensional context (on the opaque
reading) does not always preserve truth-value. E.g., the
extension of unicorn is the same as the extension of 13leaf clover (both are the empty set in the actual world).
Substituting a thirteen-leaf clover for a unicorn in (11)
preserves truth-value. The same substitution in (12)
might not.
Examples of verbs taking intentional direct
objects: seek, owe, need, lack, prevent, resemble, want,
look for, request, demand.
3.1.2. The classical analysis and its problems.
Quine (1960) argued that seek should be
decomposed into try to find. He argued that
intensionality is (in general) the result of embedding
under an intensional operator, such as the verb try.
Within Caroline try [Caroline find x] , there are then
two places a quantifier phrase could take its scope: the
higher clause, giving the transparent reading, and the
lower clause, giving the opaque reading.
seek’ (x, ^Q) Æ try’ (x, ^[Q(λy find’ (x,y))]). (13)
So Montague treats a verb like seek as denoting a
relation between an individual and an intensional
generalized quantifier. The transparent reading results
from “quantifying in”.
But there are problems with Quine’s and
Montague’s classical analyses. Among other problems,
(Zimmermann 1993) points out an overgeneration
problem with Montague’s (and Quine’s) account, in that
true quantifier phrases are normally unambiguously
“transparent” after intensional transitive verbs like
compare, seek, although they are ambiguous in
constructions like try to find. Simple indefinites with a,
on the other hand, are indeed ambiguous with
intensional verbs. Compare:
(a) Arnim compares himself to a pig.
(ambiguous)
(b) Arnim compares himself to each pig.
(unambiguously transparent)
(14)
(a) Alain is seeking a comic book.
(ambiguous)
(b) Alain is seeking each comic book.
(unambiguous; lacks ambiguity of (c))
(c) Alain is trying to find each comic book.
(ambiguous)
(15)
3.1.3. Zimmermann’s alternative account.
Zimmermann argues that we can capture the
relevant generalizations once we note that definites and
indefinites, which do receive opaque readings with
intensional verbs, correspond, in a way he makes
precise, to properties, type <s,<e,t>>. Zimmermann’s
proposal is that a verb like seek denotes a relation
between an individual and a property. So seek a
unicorn would be interpreted as (16):
seek’(^unicorn’) (where ^ is Montague’s
‘intension operator’)
(16)
This would be a case of NP type-shifting by
coercion: seek demands a property-type argument, and
we know that indefinite NPs easily shift into <s,<e,t>>
readings, as was shown for predicate nominals and the
PRED-argument of consider in (Partee 1986).
For the transparent, or specific, or de re, reading,
Zimmermann gives an analysis (details omitted here)
involving “quantifying in”, similar to the analysis in
(Partee 1986) for Edwin Williams’ example “This house
has been every color”. Zimmermann thus has a solution
to the overgeneration problem.
3.2. McNally 1995. “Bare plurals in Spanish are
interpreted as properties.”
Bare plurals in Spanish differ from bare plurals in
English in several ways; and their distribution and
interpretation is not the same as that of overtly
indefinite Spanish NPs. McNally (1995) proposes that
Spanish bare plurals are uniformly interpreted as
properties.
It is interesting to compare McNally’s analysis of
the Spanish bare plurals as properties with
Zimmermann’s analysis of the objects of opaque verbs
as properties. In the bare plural analysis, it is the NPs
that are specified as being of property type; they
combine with ordinary verbs that take ordinary e-type
arguments, and the verbs shift to accommodate these
arguments, building in an existential quantifier to bind
the e-type argument the verb was looking for: this is a
case of incorporation. In Zimmermann’s analysis of the
opaque verbs, it is the verbs that are semantically
special: they demand a property-type argument rather
than an e-type argument; so the NPs have to shift to get
a property-type meaning in order to occur there, and
those that can’t don’t get opaque readings.
It is also interesting to compare McNally’s and
other similar analyses along the dimension of
independence/non-independence
of
the
NP
interpretation, where maximal non-independence means
some kind of incorporation. On McNally’s analysis,
bare plurals have obligatorily narrowest scope, since the
existential quantifier is packed into the shifted meaning
of the verb. And the bare plural has no “discourse
referent”, which accounts for much of its ‘decreased
referentiality’ and non-independence.
4. Russian Genitive of Negation
Hypothesis: Wherever we see Nom/Gen and
Acc/Gen alternation (both under negation and under
intensional verbs), Nom or Acc represents an ordinary
e-type argument position (‘referential’; and may be
quantified), whereas a Gen NP is always interpreted as
property-type: <e,t>, or <s,<e,t>>.
In the case of the intensional verbs like ždat’, this
connects to the work of (Zimmermann 1993). It also
connects to the work of Helen de Hoop (1989, 1990,
1992). She argued for a distinction between “weak
case” and “strong case” for direct objects in Germanic
languages, with both syntactic and semantic properties.
Objects with “strong case” can move to topic position,
can escape the scope of various operators, and are
interpreted as e-type (or as generalized quantifiers if
they are quantified). Objects with “weak case” cannot
move far from the verb; they have to stay inside the VP,
and consequently they fall under the scope of any
operators that affect the VP; and they are interpreted
quasi-adverbially.
A third, similar, connection to the work of van
Geenhoven (1995, 1998), who treats ‘weak’ object NPs
in West Greenlandic as “incorporated to the verb”: they
are not fully independent objects, but get an existential
quantifier from the verb, similarly to McNally’s
treatment of Spanish bare plurals.
This hypothesis is still speculative at this stage and
requires further research.
References.
1) Barwise, J., and Cooper, R. 1981.
Generalized quantifiers and natural
language. // Linguistics and Philosophy
4:159-219. Reprinted in Portner and
Partee, eds., 2002, 75-126.
2) van Geenhoven, V. 1995. Semantic
incorporation: a uniform semantics for
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West
Germanic
bare
plural
configurations. // In CLS 31: Papers from
the Thirty First Meeting of the Chicago
Linguistic Society. Chicago: Chicago
Linguistic Society.
3) Van Geenhoven, V. 1998. Semantic
Incorporation
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Indefinite
Descriptions: Semantic and Syntactic
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